arXiv subjects

Ajit Patel

Publications and source records attributed to Ajit Patel.

2 recordsLinked to original sources

arXiv2018

A priori error analysis of the $hp$-mortar FEM for parabolic problems

In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms. The superconvergence results for the solution of the semidiscrete problem are studied in an eqivalent negative norm, with an extra regularity assumption. Numerical experiments are conducted to validate the theoretical findings.

math.AP↗

arXiv2017

Convergence results with natural norms: Stabilized Lagrange multiplier method for elliptic interface problems

A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar method is alleviated by introducing penalty terms in the formulation. Optimal convergence results are established in natural norm which is independent of mesh. Numerical experiments are conducted in support of the theoretical derivations.

math.NA↗